We present a global mesh optimization framework based on a Conditional Markov Random Fied (CMRF or CRF) model suited for 3D triangular meshes of arbitrary topology. The remeshing task is formulated as a Bayesian estimation problem including data attached terms measuring the fidelity to the original mesh as well as a prior favoring high quality triangles. Since the best solution for vertex relocation is strongly related to the mesh connectivity, our approach iteratively modifies the mesh structure (connectivity plus vertex addition/removal) as well as the vertex positions, which are moved according to a well-defined energy function resulting from the CMRF model. Good solutions for the proposed model are obtained by a discrete graph cut algorithm examining global combinations of local candidates. Results on various 3D meshes compare favorably to recent state-of-the-art algorithms regarding the trade-off between triangle shape improvement and surface fidelity. Applications of this work mainly consist in regularizing meshes for numerical simulations and for improving mesh rendering.